On the invariant manifolds of the fixed point of a second order nonlinear difference equation
Abstract
This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equation xn+1 = α + β xn-1+xn-1/xn, where α>0, 0≤slant β <1 and the initial conditions x-1 and x0 are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported by some numerical examples.
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